removed lapack 3.6.0
This commit is contained in:
Werner Saar
@@ -1,223 +0,0 @@
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C> \brief \b CGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX A( LDA, * )
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* ..
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*
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* Purpose
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* =======
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*
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C>\details \b Purpose:
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C>\verbatim
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C>
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C> CGETRF computes an LU factorization of a general M-by-N matrix A
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C> using partial pivoting with row interchanges.
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C>
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C> The factorization has the form
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C> A = P * L * U
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C> where P is a permutation matrix, L is lower triangular with unit
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C> diagonal elements (lower trapezoidal if m > n), and U is upper
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C> triangular (upper trapezoidal if m < n).
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C>
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C> This is the Crout Level 3 BLAS version of the algorithm.
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C>
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C>\endverbatim
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*
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* Arguments:
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* ==========
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*
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C> \param[in] M
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C> \verbatim
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C> M is INTEGER
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C> The number of rows of the matrix A. M >= 0.
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C> \endverbatim
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C>
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C> \param[in] N
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C> \verbatim
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C> N is INTEGER
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C> The number of columns of the matrix A. N >= 0.
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C> \endverbatim
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C>
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C> \param[in,out] A
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C> \verbatim
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C> A is COMPLEX array, dimension (LDA,N)
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C> On entry, the M-by-N matrix to be factored.
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C> On exit, the factors L and U from the factorization
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C> A = P*L*U; the unit diagonal elements of L are not stored.
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C> \endverbatim
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C>
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C> \param[in] LDA
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C> \verbatim
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C> LDA is INTEGER
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C> The leading dimension of the array A. LDA >= max(1,M).
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C> \endverbatim
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C>
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C> \param[out] IPIV
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C> \verbatim
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C> IPIV is INTEGER array, dimension (min(M,N))
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C> The pivot indices; for 1 <= i <= min(M,N), row i of the
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C> matrix was interchanged with row IPIV(i).
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C> \endverbatim
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C>
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C> \param[out] INFO
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C> \verbatim
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C> INFO is INTEGER
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C> = 0: successful exit
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C> < 0: if INFO = -i, the i-th argument had an illegal value
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C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
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C> has been completed, but the factor U is exactly
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C> singular, and division by zero will occur if it is used
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C> to solve a system of equations.
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C> \endverbatim
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C>
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*
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* Authors:
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* ========
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*
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C> \author Univ. of Tennessee
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C> \author Univ. of California Berkeley
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C> \author Univ. of Colorado Denver
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C> \author NAG Ltd.
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*
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C> \date November 2011
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*
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C> \ingroup variantsGEcomputational
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*
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* =====================================================================
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SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
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*
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* -- LAPACK computational routine (version 3.1) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX A( LDA, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX ONE
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PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, IINFO, J, JB, NB
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEMM, CGETF2, CLASWP, CTRSM, XERBLA
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CGETRF', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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* Determine the block size for this environment.
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*
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NB = ILAENV( 1, 'CGETRF', ' ', M, N, -1, -1 )
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IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
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*
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* Use unblocked code.
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*
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CALL CGETF2( M, N, A, LDA, IPIV, INFO )
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ELSE
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*
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* Use blocked code.
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*
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DO 20 J = 1, MIN( M, N ), NB
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JB = MIN( MIN( M, N )-J+1, NB )
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*
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* Update current block.
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*
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CALL CGEMM( 'No transpose', 'No transpose',
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$ M-J+1, JB, J-1, -ONE,
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$ A( J, 1 ), LDA, A( 1, J ), LDA, ONE,
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$ A( J, J ), LDA )
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*
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* Factor diagonal and subdiagonal blocks and test for exact
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* singularity.
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*
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CALL CGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
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*
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* Adjust INFO and the pivot indices.
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*
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IF( INFO.EQ.0 .AND. IINFO.GT.0 )
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$ INFO = IINFO + J - 1
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DO 10 I = J, MIN( M, J+JB-1 )
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IPIV( I ) = J - 1 + IPIV( I )
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10 CONTINUE
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*
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* Apply interchanges to column 1:J-1
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*
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CALL CLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
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*
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IF ( J+JB.LE.N ) THEN
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*
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* Apply interchanges to column J+JB:N
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*
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CALL CLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
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$ IPIV, 1 )
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*
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CALL CGEMM( 'No transpose', 'No transpose',
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$ JB, N-J-JB+1, J-1, -ONE,
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$ A( J, 1 ), LDA, A( 1, J+JB ), LDA, ONE,
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$ A( J, J+JB ), LDA )
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*
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* Compute block row of U.
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*
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CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
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$ JB, N-J-JB+1, ONE, A( J, J ), LDA,
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$ A( J, J+JB ), LDA )
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END IF
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20 CONTINUE
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END IF
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RETURN
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*
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* End of CGETRF
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*
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END
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@@ -1,223 +0,0 @@
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C> \brief \b DGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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||||
* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* DOUBLE PRECISION A( LDA, * )
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* ..
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*
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* Purpose
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* =======
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*
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C>\details \b Purpose:
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C>\verbatim
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C>
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C> DGETRF computes an LU factorization of a general M-by-N matrix A
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C> using partial pivoting with row interchanges.
|
||||
C>
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||||
C> The factorization has the form
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C> A = P * L * U
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C> where P is a permutation matrix, L is lower triangular with unit
|
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C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
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C> This is the Crout Level 3 BLAS version of the algorithm.
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C>
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C>\endverbatim
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*
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* Arguments:
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* ==========
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*
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C> \param[in] M
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C> \verbatim
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C> M is INTEGER
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C> The number of rows of the matrix A. M >= 0.
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C> \endverbatim
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C>
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C> \param[in] N
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C> \verbatim
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C> N is INTEGER
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C> The number of columns of the matrix A. N >= 0.
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C> \endverbatim
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C>
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C> \param[in,out] A
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C> \verbatim
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C> A is DOUBLE PRECISION array, dimension (LDA,N)
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C> On entry, the M-by-N matrix to be factored.
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C> On exit, the factors L and U from the factorization
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C> A = P*L*U; the unit diagonal elements of L are not stored.
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C> \endverbatim
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C>
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C> \param[in] LDA
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C> \verbatim
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C> LDA is INTEGER
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C> The leading dimension of the array A. LDA >= max(1,M).
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C> \endverbatim
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C>
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C> \param[out] IPIV
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C> \verbatim
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C> IPIV is INTEGER array, dimension (min(M,N))
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C> The pivot indices; for 1 <= i <= min(M,N), row i of the
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C> matrix was interchanged with row IPIV(i).
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C> \endverbatim
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C>
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C> \param[out] INFO
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C> \verbatim
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C> INFO is INTEGER
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C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
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C> has been completed, but the factor U is exactly
|
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C> singular, and division by zero will occur if it is used
|
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C> to solve a system of equations.
|
||||
C> \endverbatim
|
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C>
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*
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||||
* Authors:
|
||||
* ========
|
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*
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C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
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*
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C> \date November 2011
|
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*
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C> \ingroup variantsGEcomputational
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*
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* =====================================================================
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SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
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*
|
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* -- LAPACK computational routine (version 3.1) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
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* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
|
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INTEGER IPIV( * )
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DOUBLE PRECISION A( LDA, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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||||
DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D+0 )
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* ..
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||||
* .. Local Scalars ..
|
||||
INTEGER I, IINFO, J, JB, NB
|
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* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL DGEMM, DGETF2, DLASWP, DTRSM, XERBLA
|
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* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
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INFO = -2
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||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
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INFO = -4
|
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END IF
|
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGETRF', -INFO )
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RETURN
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||||
END IF
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*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
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$ RETURN
|
||||
*
|
||||
* Determine the block size for this environment.
|
||||
*
|
||||
NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 )
|
||||
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
|
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*
|
||||
* Use unblocked code.
|
||||
*
|
||||
CALL DGETF2( M, N, A, LDA, IPIV, INFO )
|
||||
ELSE
|
||||
*
|
||||
* Use blocked code.
|
||||
*
|
||||
DO 20 J = 1, MIN( M, N ), NB
|
||||
JB = MIN( MIN( M, N )-J+1, NB )
|
||||
*
|
||||
* Update current block.
|
||||
*
|
||||
CALL DGEMM( 'No transpose', 'No transpose',
|
||||
$ M-J+1, JB, J-1, -ONE,
|
||||
$ A( J, 1 ), LDA, A( 1, J ), LDA, ONE,
|
||||
$ A( J, J ), LDA )
|
||||
|
||||
*
|
||||
* Factor diagonal and subdiagonal blocks and test for exact
|
||||
* singularity.
|
||||
*
|
||||
CALL DGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
|
||||
*
|
||||
* Adjust INFO and the pivot indices.
|
||||
*
|
||||
IF( INFO.EQ.0 .AND. IINFO.GT.0 )
|
||||
$ INFO = IINFO + J - 1
|
||||
DO 10 I = J, MIN( M, J+JB-1 )
|
||||
IPIV( I ) = J - 1 + IPIV( I )
|
||||
10 CONTINUE
|
||||
*
|
||||
* Apply interchanges to column 1:J-1
|
||||
*
|
||||
CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
|
||||
*
|
||||
IF ( J+JB.LE.N ) THEN
|
||||
*
|
||||
* Apply interchanges to column J+JB:N
|
||||
*
|
||||
CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
|
||||
$ IPIV, 1 )
|
||||
*
|
||||
CALL DGEMM( 'No transpose', 'No transpose',
|
||||
$ JB, N-J-JB+1, J-1, -ONE,
|
||||
$ A( J, 1 ), LDA, A( 1, J+JB ), LDA, ONE,
|
||||
$ A( J, J+JB ), LDA )
|
||||
*
|
||||
* Compute block row of U.
|
||||
*
|
||||
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ JB, N-J-JB+1, ONE, A( J, J ), LDA,
|
||||
$ A( J, J+JB ), LDA )
|
||||
END IF
|
||||
|
||||
20 CONTINUE
|
||||
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,223 +0,0 @@
|
||||
C> \brief \b SGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* REAL A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> SGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This is the Crout Level 3 BLAS version of the algorithm.
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is REAL array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.1) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
REAL A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
REAL ONE
|
||||
PARAMETER ( ONE = 1.0E+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
INTEGER I, IINFO, J, JB, NB
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL SGEMM, SGETF2, SLASWP, STRSM, XERBLA
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'SGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Determine the block size for this environment.
|
||||
*
|
||||
NB = ILAENV( 1, 'SGETRF', ' ', M, N, -1, -1 )
|
||||
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
|
||||
*
|
||||
* Use unblocked code.
|
||||
*
|
||||
CALL SGETF2( M, N, A, LDA, IPIV, INFO )
|
||||
ELSE
|
||||
*
|
||||
* Use blocked code.
|
||||
*
|
||||
DO 20 J = 1, MIN( M, N ), NB
|
||||
JB = MIN( MIN( M, N )-J+1, NB )
|
||||
*
|
||||
* Update current block.
|
||||
*
|
||||
CALL SGEMM( 'No transpose', 'No transpose',
|
||||
$ M-J+1, JB, J-1, -ONE,
|
||||
$ A( J, 1 ), LDA, A( 1, J ), LDA, ONE,
|
||||
$ A( J, J ), LDA )
|
||||
|
||||
*
|
||||
* Factor diagonal and subdiagonal blocks and test for exact
|
||||
* singularity.
|
||||
*
|
||||
CALL SGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
|
||||
*
|
||||
* Adjust INFO and the pivot indices.
|
||||
*
|
||||
IF( INFO.EQ.0 .AND. IINFO.GT.0 )
|
||||
$ INFO = IINFO + J - 1
|
||||
DO 10 I = J, MIN( M, J+JB-1 )
|
||||
IPIV( I ) = J - 1 + IPIV( I )
|
||||
10 CONTINUE
|
||||
*
|
||||
* Apply interchanges to column 1:J-1
|
||||
*
|
||||
CALL SLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
|
||||
*
|
||||
IF ( J+JB.LE.N ) THEN
|
||||
*
|
||||
* Apply interchanges to column J+JB:N
|
||||
*
|
||||
CALL SLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
|
||||
$ IPIV, 1 )
|
||||
*
|
||||
CALL SGEMM( 'No transpose', 'No transpose',
|
||||
$ JB, N-J-JB+1, J-1, -ONE,
|
||||
$ A( J, 1 ), LDA, A( 1, J+JB ), LDA, ONE,
|
||||
$ A( J, J+JB ), LDA )
|
||||
*
|
||||
* Compute block row of U.
|
||||
*
|
||||
CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ JB, N-J-JB+1, ONE, A( J, J ), LDA,
|
||||
$ A( J, J+JB ), LDA )
|
||||
END IF
|
||||
|
||||
20 CONTINUE
|
||||
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of SGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,223 +0,0 @@
|
||||
C> \brief \b ZGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* COMPLEX*16 A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> ZGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This is the Crout Level 3 BLAS version of the algorithm.
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is COMPLEX*16 array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.1) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
COMPLEX*16 A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
COMPLEX*16 ONE
|
||||
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
INTEGER I, IINFO, J, JB, NB
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL ZGEMM, ZGETF2, ZLASWP, ZTRSM, XERBLA
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'ZGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Determine the block size for this environment.
|
||||
*
|
||||
NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 )
|
||||
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
|
||||
*
|
||||
* Use unblocked code.
|
||||
*
|
||||
CALL ZGETF2( M, N, A, LDA, IPIV, INFO )
|
||||
ELSE
|
||||
*
|
||||
* Use blocked code.
|
||||
*
|
||||
DO 20 J = 1, MIN( M, N ), NB
|
||||
JB = MIN( MIN( M, N )-J+1, NB )
|
||||
*
|
||||
* Update current block.
|
||||
*
|
||||
CALL ZGEMM( 'No transpose', 'No transpose',
|
||||
$ M-J+1, JB, J-1, -ONE,
|
||||
$ A( J, 1 ), LDA, A( 1, J ), LDA, ONE,
|
||||
$ A( J, J ), LDA )
|
||||
|
||||
*
|
||||
* Factor diagonal and subdiagonal blocks and test for exact
|
||||
* singularity.
|
||||
*
|
||||
CALL ZGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
|
||||
*
|
||||
* Adjust INFO and the pivot indices.
|
||||
*
|
||||
IF( INFO.EQ.0 .AND. IINFO.GT.0 )
|
||||
$ INFO = IINFO + J - 1
|
||||
DO 10 I = J, MIN( M, J+JB-1 )
|
||||
IPIV( I ) = J - 1 + IPIV( I )
|
||||
10 CONTINUE
|
||||
*
|
||||
* Apply interchanges to column 1:J-1
|
||||
*
|
||||
CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
|
||||
*
|
||||
IF ( J+JB.LE.N ) THEN
|
||||
*
|
||||
* Apply interchanges to column J+JB:N
|
||||
*
|
||||
CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
|
||||
$ IPIV, 1 )
|
||||
*
|
||||
CALL ZGEMM( 'No transpose', 'No transpose',
|
||||
$ JB, N-J-JB+1, J-1, -ONE,
|
||||
$ A( J, 1 ), LDA, A( 1, J+JB ), LDA, ONE,
|
||||
$ A( J, J+JB ), LDA )
|
||||
*
|
||||
* Compute block row of U.
|
||||
*
|
||||
CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ JB, N-J-JB+1, ONE, A( J, J ), LDA,
|
||||
$ A( J, J+JB ), LDA )
|
||||
END IF
|
||||
|
||||
20 CONTINUE
|
||||
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of ZGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,248 +0,0 @@
|
||||
C> \brief \b CGETRF VARIANT: left-looking Level 3 BLAS version of the algorithm.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* COMPLEX A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> CGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This is the left-looking Level 3 BLAS version of the algorithm.
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is COMPLEX array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.1) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
COMPLEX A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
COMPLEX ONE
|
||||
PARAMETER ( ONE = (1.0E+0, 0.0E+0) )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
INTEGER I, IINFO, J, JB, K, NB
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL CGEMM, CGETF2, CLASWP, CTRSM, XERBLA
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'CGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Determine the block size for this environment.
|
||||
*
|
||||
NB = ILAENV( 1, 'CGETRF', ' ', M, N, -1, -1 )
|
||||
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
|
||||
*
|
||||
* Use unblocked code.
|
||||
*
|
||||
CALL CGETF2( M, N, A, LDA, IPIV, INFO )
|
||||
|
||||
ELSE
|
||||
*
|
||||
* Use blocked code.
|
||||
*
|
||||
DO 20 J = 1, MIN( M, N ), NB
|
||||
JB = MIN( MIN( M, N )-J+1, NB )
|
||||
*
|
||||
*
|
||||
* Update before factoring the current panel
|
||||
*
|
||||
DO 30 K = 1, J-NB, NB
|
||||
*
|
||||
* Apply interchanges to rows K:K+NB-1.
|
||||
*
|
||||
CALL CLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 )
|
||||
*
|
||||
* Compute block row of U.
|
||||
*
|
||||
CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ NB, JB, ONE, A( K, K ), LDA,
|
||||
$ A( K, J ), LDA )
|
||||
*
|
||||
* Update trailing submatrix.
|
||||
*
|
||||
CALL CGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, JB, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, J ), LDA, ONE,
|
||||
$ A( K+NB, J ), LDA )
|
||||
30 CONTINUE
|
||||
*
|
||||
* Factor diagonal and subdiagonal blocks and test for exact
|
||||
* singularity.
|
||||
*
|
||||
CALL CGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
|
||||
*
|
||||
* Adjust INFO and the pivot indices.
|
||||
*
|
||||
IF( INFO.EQ.0 .AND. IINFO.GT.0 )
|
||||
$ INFO = IINFO + J - 1
|
||||
DO 10 I = J, MIN( M, J+JB-1 )
|
||||
IPIV( I ) = J - 1 + IPIV( I )
|
||||
10 CONTINUE
|
||||
*
|
||||
20 CONTINUE
|
||||
|
||||
*
|
||||
* Apply interchanges to the left-overs
|
||||
*
|
||||
DO 40 K = 1, MIN( M, N ), NB
|
||||
CALL CLASWP( K-1, A( 1, 1 ), LDA, K,
|
||||
$ MIN (K+NB-1, MIN ( M, N )), IPIV, 1 )
|
||||
40 CONTINUE
|
||||
*
|
||||
* Apply update to the M+1:N columns when N > M
|
||||
*
|
||||
IF ( N.GT.M ) THEN
|
||||
|
||||
CALL CLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 )
|
||||
|
||||
DO 50 K = 1, M, NB
|
||||
|
||||
JB = MIN( M-K+1, NB )
|
||||
*
|
||||
CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ JB, N-M, ONE, A( K, K ), LDA,
|
||||
$ A( K, M+1 ), LDA )
|
||||
|
||||
*
|
||||
IF ( K+NB.LE.M ) THEN
|
||||
CALL CGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, N-M, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, M+1 ), LDA, ONE,
|
||||
$ A( K+NB, M+1 ), LDA )
|
||||
END IF
|
||||
50 CONTINUE
|
||||
END IF
|
||||
*
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of CGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,247 +0,0 @@
|
||||
C> \brief \b DGETRF VARIANT: left-looking Level 3 BLAS version of the algorithm.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* DOUBLE PRECISION A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> DGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This is the left-looking Level 3 BLAS version of the algorithm.
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is DOUBLE PRECISION array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.1) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
DOUBLE PRECISION A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
DOUBLE PRECISION ONE
|
||||
PARAMETER ( ONE = 1.0D+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
INTEGER I, IINFO, J, JB, K, NB
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL DGEMM, DGETF2, DLASWP, DTRSM, XERBLA
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'DGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Determine the block size for this environment.
|
||||
*
|
||||
NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 )
|
||||
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
|
||||
*
|
||||
* Use unblocked code.
|
||||
*
|
||||
CALL DGETF2( M, N, A, LDA, IPIV, INFO )
|
||||
|
||||
ELSE
|
||||
*
|
||||
* Use blocked code.
|
||||
*
|
||||
DO 20 J = 1, MIN( M, N ), NB
|
||||
JB = MIN( MIN( M, N )-J+1, NB )
|
||||
*
|
||||
* Update before factoring the current panel
|
||||
*
|
||||
DO 30 K = 1, J-NB, NB
|
||||
*
|
||||
* Apply interchanges to rows K:K+NB-1.
|
||||
*
|
||||
CALL DLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 )
|
||||
*
|
||||
* Compute block row of U.
|
||||
*
|
||||
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ NB, JB, ONE, A( K, K ), LDA,
|
||||
$ A( K, J ), LDA )
|
||||
*
|
||||
* Update trailing submatrix.
|
||||
*
|
||||
CALL DGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, JB, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, J ), LDA, ONE,
|
||||
$ A( K+NB, J ), LDA )
|
||||
30 CONTINUE
|
||||
*
|
||||
* Factor diagonal and subdiagonal blocks and test for exact
|
||||
* singularity.
|
||||
*
|
||||
CALL DGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
|
||||
*
|
||||
* Adjust INFO and the pivot indices.
|
||||
*
|
||||
IF( INFO.EQ.0 .AND. IINFO.GT.0 )
|
||||
$ INFO = IINFO + J - 1
|
||||
DO 10 I = J, MIN( M, J+JB-1 )
|
||||
IPIV( I ) = J - 1 + IPIV( I )
|
||||
10 CONTINUE
|
||||
*
|
||||
20 CONTINUE
|
||||
|
||||
*
|
||||
* Apply interchanges to the left-overs
|
||||
*
|
||||
DO 40 K = 1, MIN( M, N ), NB
|
||||
CALL DLASWP( K-1, A( 1, 1 ), LDA, K,
|
||||
$ MIN (K+NB-1, MIN ( M, N )), IPIV, 1 )
|
||||
40 CONTINUE
|
||||
*
|
||||
* Apply update to the M+1:N columns when N > M
|
||||
*
|
||||
IF ( N.GT.M ) THEN
|
||||
|
||||
CALL DLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 )
|
||||
|
||||
DO 50 K = 1, M, NB
|
||||
|
||||
JB = MIN( M-K+1, NB )
|
||||
*
|
||||
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ JB, N-M, ONE, A( K, K ), LDA,
|
||||
$ A( K, M+1 ), LDA )
|
||||
|
||||
*
|
||||
IF ( K+NB.LE.M ) THEN
|
||||
CALL DGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, N-M, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, M+1 ), LDA, ONE,
|
||||
$ A( K+NB, M+1 ), LDA )
|
||||
END IF
|
||||
50 CONTINUE
|
||||
END IF
|
||||
*
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,248 +0,0 @@
|
||||
C> \brief \b SGETRF VARIANT: left-looking Level 3 BLAS version of the algorithm.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* REAL A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> SGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This is the left-looking Level 3 BLAS version of the algorithm.
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is REAL array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.1) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
REAL A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
REAL ONE
|
||||
PARAMETER ( ONE = 1.0E+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
INTEGER I, IINFO, J, JB, K, NB
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL SGEMM, SGETF2, SLASWP, STRSM, XERBLA
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'SGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Determine the block size for this environment.
|
||||
*
|
||||
NB = ILAENV( 1, 'SGETRF', ' ', M, N, -1, -1 )
|
||||
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
|
||||
*
|
||||
* Use unblocked code.
|
||||
*
|
||||
CALL SGETF2( M, N, A, LDA, IPIV, INFO )
|
||||
|
||||
ELSE
|
||||
*
|
||||
* Use blocked code.
|
||||
*
|
||||
DO 20 J = 1, MIN( M, N ), NB
|
||||
JB = MIN( MIN( M, N )-J+1, NB )
|
||||
*
|
||||
*
|
||||
* Update before factoring the current panel
|
||||
*
|
||||
DO 30 K = 1, J-NB, NB
|
||||
*
|
||||
* Apply interchanges to rows K:K+NB-1.
|
||||
*
|
||||
CALL SLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 )
|
||||
*
|
||||
* Compute block row of U.
|
||||
*
|
||||
CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ NB, JB, ONE, A( K, K ), LDA,
|
||||
$ A( K, J ), LDA )
|
||||
*
|
||||
* Update trailing submatrix.
|
||||
*
|
||||
CALL SGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, JB, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, J ), LDA, ONE,
|
||||
$ A( K+NB, J ), LDA )
|
||||
30 CONTINUE
|
||||
*
|
||||
* Factor diagonal and subdiagonal blocks and test for exact
|
||||
* singularity.
|
||||
*
|
||||
CALL SGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
|
||||
*
|
||||
* Adjust INFO and the pivot indices.
|
||||
*
|
||||
IF( INFO.EQ.0 .AND. IINFO.GT.0 )
|
||||
$ INFO = IINFO + J - 1
|
||||
DO 10 I = J, MIN( M, J+JB-1 )
|
||||
IPIV( I ) = J - 1 + IPIV( I )
|
||||
10 CONTINUE
|
||||
*
|
||||
20 CONTINUE
|
||||
|
||||
*
|
||||
* Apply interchanges to the left-overs
|
||||
*
|
||||
DO 40 K = 1, MIN( M, N ), NB
|
||||
CALL SLASWP( K-1, A( 1, 1 ), LDA, K,
|
||||
$ MIN (K+NB-1, MIN ( M, N )), IPIV, 1 )
|
||||
40 CONTINUE
|
||||
*
|
||||
* Apply update to the M+1:N columns when N > M
|
||||
*
|
||||
IF ( N.GT.M ) THEN
|
||||
|
||||
CALL SLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 )
|
||||
|
||||
DO 50 K = 1, M, NB
|
||||
|
||||
JB = MIN( M-K+1, NB )
|
||||
*
|
||||
CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ JB, N-M, ONE, A( K, K ), LDA,
|
||||
$ A( K, M+1 ), LDA )
|
||||
|
||||
*
|
||||
IF ( K+NB.LE.M ) THEN
|
||||
CALL SGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, N-M, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, M+1 ), LDA, ONE,
|
||||
$ A( K+NB, M+1 ), LDA )
|
||||
END IF
|
||||
50 CONTINUE
|
||||
END IF
|
||||
*
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of SGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,248 +0,0 @@
|
||||
C> \brief \b ZGETRF VARIANT: left-looking Level 3 BLAS version of the algorithm.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* COMPLEX*16 A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> ZGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This is the left-looking Level 3 BLAS version of the algorithm.
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is COMPLEX*16 array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.1) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
COMPLEX*16 A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
COMPLEX*16 ONE
|
||||
PARAMETER ( ONE = (1.0D+0, 0.0D+0) )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
INTEGER I, IINFO, J, JB, K, NB
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL ZGEMM, ZGETF2, ZLASWP, ZTRSM, XERBLA
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
INTEGER ILAENV
|
||||
EXTERNAL ILAENV
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'ZGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Determine the block size for this environment.
|
||||
*
|
||||
NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 )
|
||||
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
|
||||
*
|
||||
* Use unblocked code.
|
||||
*
|
||||
CALL ZGETF2( M, N, A, LDA, IPIV, INFO )
|
||||
|
||||
ELSE
|
||||
*
|
||||
* Use blocked code.
|
||||
*
|
||||
DO 20 J = 1, MIN( M, N ), NB
|
||||
JB = MIN( MIN( M, N )-J+1, NB )
|
||||
*
|
||||
*
|
||||
* Update before factoring the current panel
|
||||
*
|
||||
DO 30 K = 1, J-NB, NB
|
||||
*
|
||||
* Apply interchanges to rows K:K+NB-1.
|
||||
*
|
||||
CALL ZLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 )
|
||||
*
|
||||
* Compute block row of U.
|
||||
*
|
||||
CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ NB, JB, ONE, A( K, K ), LDA,
|
||||
$ A( K, J ), LDA )
|
||||
*
|
||||
* Update trailing submatrix.
|
||||
*
|
||||
CALL ZGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, JB, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, J ), LDA, ONE,
|
||||
$ A( K+NB, J ), LDA )
|
||||
30 CONTINUE
|
||||
*
|
||||
* Factor diagonal and subdiagonal blocks and test for exact
|
||||
* singularity.
|
||||
*
|
||||
CALL ZGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
|
||||
*
|
||||
* Adjust INFO and the pivot indices.
|
||||
*
|
||||
IF( INFO.EQ.0 .AND. IINFO.GT.0 )
|
||||
$ INFO = IINFO + J - 1
|
||||
DO 10 I = J, MIN( M, J+JB-1 )
|
||||
IPIV( I ) = J - 1 + IPIV( I )
|
||||
10 CONTINUE
|
||||
*
|
||||
20 CONTINUE
|
||||
|
||||
*
|
||||
* Apply interchanges to the left-overs
|
||||
*
|
||||
DO 40 K = 1, MIN( M, N ), NB
|
||||
CALL ZLASWP( K-1, A( 1, 1 ), LDA, K,
|
||||
$ MIN (K+NB-1, MIN ( M, N )), IPIV, 1 )
|
||||
40 CONTINUE
|
||||
*
|
||||
* Apply update to the M+1:N columns when N > M
|
||||
*
|
||||
IF ( N.GT.M ) THEN
|
||||
|
||||
CALL ZLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 )
|
||||
|
||||
DO 50 K = 1, M, NB
|
||||
|
||||
JB = MIN( M-K+1, NB )
|
||||
*
|
||||
CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
|
||||
$ JB, N-M, ONE, A( K, K ), LDA,
|
||||
$ A( K, M+1 ), LDA )
|
||||
|
||||
*
|
||||
IF ( K+NB.LE.M ) THEN
|
||||
CALL ZGEMM( 'No transpose', 'No transpose',
|
||||
$ M-K-NB+1, N-M, NB, -ONE,
|
||||
$ A( K+NB, K ), LDA, A( K, M+1 ), LDA, ONE,
|
||||
$ A( K+NB, M+1 ), LDA )
|
||||
END IF
|
||||
50 CONTINUE
|
||||
END IF
|
||||
*
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of ZGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,281 +0,0 @@
|
||||
C> \brief \b CGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE CGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* COMPLEX A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> CGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This code implements an iterative version of Sivan Toledo's recursive
|
||||
C> LU algorithm[1]. For square matrices, this iterative versions should
|
||||
C> be within a factor of two of the optimum number of memory transfers.
|
||||
C>
|
||||
C> The pattern is as follows, with the large blocks of U being updated
|
||||
C> in one call to DTRSM, and the dotted lines denoting sections that
|
||||
C> have had all pending permutations applied:
|
||||
C>
|
||||
C> 1 2 3 4 5 6 7 8
|
||||
C> +-+-+---+-------+------
|
||||
C> | |1| | |
|
||||
C> |.+-+ 2 | |
|
||||
C> | | | | |
|
||||
C> |.|.+-+-+ 4 |
|
||||
C> | | | |1| |
|
||||
C> | | |.+-+ |
|
||||
C> | | | | | |
|
||||
C> |.|.|.|.+-+-+---+ 8
|
||||
C> | | | | | |1| |
|
||||
C> | | | | |.+-+ 2 |
|
||||
C> | | | | | | | |
|
||||
C> | | | | |.|.+-+-+
|
||||
C> | | | | | | | |1|
|
||||
C> | | | | | | |.+-+
|
||||
C> | | | | | | | | |
|
||||
C> |.|.|.|.|.|.|.|.+-----
|
||||
C> | | | | | | | | |
|
||||
C>
|
||||
C> The 1-2-1-4-1-2-1-8-... pattern is the position of the last 1 bit in
|
||||
C> the binary expansion of the current column. Each Schur update is
|
||||
C> applied as soon as the necessary portion of U is available.
|
||||
C>
|
||||
C> [1] Toledo, S. 1997. Locality of Reference in LU Decomposition with
|
||||
C> Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997),
|
||||
C> 1065-1081. http://dx.doi.org/10.1137/S0895479896297744
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is COMPLEX array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE CGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.X) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
COMPLEX A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
COMPLEX ONE, NEGONE
|
||||
REAL ZERO
|
||||
PARAMETER ( ONE = (1.0E+0, 0.0E+0) )
|
||||
PARAMETER ( NEGONE = (-1.0E+0, 0.0E+0) )
|
||||
PARAMETER ( ZERO = 0.0E+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
REAL SFMIN, PIVMAG
|
||||
COMPLEX TMP
|
||||
INTEGER I, J, JP, NSTEP, NTOPIV, NPIVED, KAHEAD
|
||||
INTEGER KSTART, IPIVSTART, JPIVSTART, KCOLS
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
REAL SLAMCH
|
||||
INTEGER ICAMAX
|
||||
LOGICAL SISNAN
|
||||
EXTERNAL SLAMCH, ICAMAX, SISNAN
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL CTRSM, CSCAL, XERBLA, CLASWP
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN, IAND, ABS
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'CGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Compute machine safe minimum
|
||||
*
|
||||
SFMIN = SLAMCH( 'S' )
|
||||
*
|
||||
NSTEP = MIN( M, N )
|
||||
DO J = 1, NSTEP
|
||||
KAHEAD = IAND( J, -J )
|
||||
KSTART = J + 1 - KAHEAD
|
||||
KCOLS = MIN( KAHEAD, M-J )
|
||||
*
|
||||
* Find pivot.
|
||||
*
|
||||
JP = J - 1 + ICAMAX( M-J+1, A( J, J ), 1 )
|
||||
IPIV( J ) = JP
|
||||
|
||||
* Permute just this column.
|
||||
IF (JP .NE. J) THEN
|
||||
TMP = A( J, J )
|
||||
A( J, J ) = A( JP, J )
|
||||
A( JP, J ) = TMP
|
||||
END IF
|
||||
|
||||
* Apply pending permutations to L
|
||||
NTOPIV = 1
|
||||
IPIVSTART = J
|
||||
JPIVSTART = J - NTOPIV
|
||||
DO WHILE ( NTOPIV .LT. KAHEAD )
|
||||
CALL CLASWP( NTOPIV, A( 1, JPIVSTART ), LDA, IPIVSTART, J,
|
||||
$ IPIV, 1 )
|
||||
IPIVSTART = IPIVSTART - NTOPIV;
|
||||
NTOPIV = NTOPIV * 2;
|
||||
JPIVSTART = JPIVSTART - NTOPIV;
|
||||
END DO
|
||||
|
||||
* Permute U block to match L
|
||||
CALL CLASWP( KCOLS, A( 1,J+1 ), LDA, KSTART, J, IPIV, 1 )
|
||||
|
||||
* Factor the current column
|
||||
PIVMAG = ABS( A( J, J ) )
|
||||
IF( PIVMAG.NE.ZERO .AND. .NOT.SISNAN( PIVMAG ) ) THEN
|
||||
IF( PIVMAG .GE. SFMIN ) THEN
|
||||
CALL CSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
|
||||
ELSE
|
||||
DO I = 1, M-J
|
||||
A( J+I, J ) = A( J+I, J ) / A( J, J )
|
||||
END DO
|
||||
END IF
|
||||
ELSE IF( PIVMAG .EQ. ZERO .AND. INFO .EQ. 0 ) THEN
|
||||
INFO = J
|
||||
END IF
|
||||
|
||||
* Solve for U block.
|
||||
CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Unit', KAHEAD,
|
||||
$ KCOLS, ONE, A( KSTART, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA )
|
||||
* Schur complement.
|
||||
CALL CGEMM( 'No transpose', 'No transpose', M-J,
|
||||
$ KCOLS, KAHEAD, NEGONE, A( J+1, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA, ONE, A( J+1, J+1 ), LDA )
|
||||
END DO
|
||||
|
||||
* Handle pivot permutations on the way out of the recursion
|
||||
NPIVED = IAND( NSTEP, -NSTEP )
|
||||
J = NSTEP - NPIVED
|
||||
DO WHILE ( J .GT. 0 )
|
||||
NTOPIV = IAND( J, -J )
|
||||
CALL CLASWP( NTOPIV, A( 1, J-NTOPIV+1 ), LDA, J+1, NSTEP,
|
||||
$ IPIV, 1 )
|
||||
J = J - NTOPIV
|
||||
END DO
|
||||
|
||||
* If short and wide, handle the rest of the columns.
|
||||
IF ( M .LT. N ) THEN
|
||||
CALL CLASWP( N-M, A( 1, M+KCOLS+1 ), LDA, 1, M, IPIV, 1 )
|
||||
CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Unit', M,
|
||||
$ N-M, ONE, A, LDA, A( 1,M+KCOLS+1 ), LDA )
|
||||
END IF
|
||||
|
||||
RETURN
|
||||
*
|
||||
* End of CGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,277 +0,0 @@
|
||||
C> \brief \b DGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* DOUBLE PRECISION A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> DGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This code implements an iterative version of Sivan Toledo's recursive
|
||||
C> LU algorithm[1]. For square matrices, this iterative versions should
|
||||
C> be within a factor of two of the optimum number of memory transfers.
|
||||
C>
|
||||
C> The pattern is as follows, with the large blocks of U being updated
|
||||
C> in one call to DTRSM, and the dotted lines denoting sections that
|
||||
C> have had all pending permutations applied:
|
||||
C>
|
||||
C> 1 2 3 4 5 6 7 8
|
||||
C> +-+-+---+-------+------
|
||||
C> | |1| | |
|
||||
C> |.+-+ 2 | |
|
||||
C> | | | | |
|
||||
C> |.|.+-+-+ 4 |
|
||||
C> | | | |1| |
|
||||
C> | | |.+-+ |
|
||||
C> | | | | | |
|
||||
C> |.|.|.|.+-+-+---+ 8
|
||||
C> | | | | | |1| |
|
||||
C> | | | | |.+-+ 2 |
|
||||
C> | | | | | | | |
|
||||
C> | | | | |.|.+-+-+
|
||||
C> | | | | | | | |1|
|
||||
C> | | | | | | |.+-+
|
||||
C> | | | | | | | | |
|
||||
C> |.|.|.|.|.|.|.|.+-----
|
||||
C> | | | | | | | | |
|
||||
C>
|
||||
C> The 1-2-1-4-1-2-1-8-... pattern is the position of the last 1 bit in
|
||||
C> the binary expansion of the current column. Each Schur update is
|
||||
C> applied as soon as the necessary portion of U is available.
|
||||
C>
|
||||
C> [1] Toledo, S. 1997. Locality of Reference in LU Decomposition with
|
||||
C> Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997),
|
||||
C> 1065-1081. http://dx.doi.org/10.1137/S0895479896297744
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is DOUBLE PRECISION array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.X) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
DOUBLE PRECISION A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
DOUBLE PRECISION ONE, ZERO, NEGONE
|
||||
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
|
||||
PARAMETER ( NEGONE = -1.0D+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
DOUBLE PRECISION SFMIN, TMP
|
||||
INTEGER I, J, JP, NSTEP, NTOPIV, NPIVED, KAHEAD
|
||||
INTEGER KSTART, IPIVSTART, JPIVSTART, KCOLS
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
DOUBLE PRECISION DLAMCH
|
||||
INTEGER IDAMAX
|
||||
LOGICAL DISNAN
|
||||
EXTERNAL DLAMCH, IDAMAX, DISNAN
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL DTRSM, DSCAL, XERBLA, DLASWP
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN, IAND
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'DGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Compute machine safe minimum
|
||||
*
|
||||
SFMIN = DLAMCH( 'S' )
|
||||
*
|
||||
NSTEP = MIN( M, N )
|
||||
DO J = 1, NSTEP
|
||||
KAHEAD = IAND( J, -J )
|
||||
KSTART = J + 1 - KAHEAD
|
||||
KCOLS = MIN( KAHEAD, M-J )
|
||||
*
|
||||
* Find pivot.
|
||||
*
|
||||
JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 )
|
||||
IPIV( J ) = JP
|
||||
|
||||
* Permute just this column.
|
||||
IF (JP .NE. J) THEN
|
||||
TMP = A( J, J )
|
||||
A( J, J ) = A( JP, J )
|
||||
A( JP, J ) = TMP
|
||||
END IF
|
||||
|
||||
* Apply pending permutations to L
|
||||
NTOPIV = 1
|
||||
IPIVSTART = J
|
||||
JPIVSTART = J - NTOPIV
|
||||
DO WHILE ( NTOPIV .LT. KAHEAD )
|
||||
CALL DLASWP( NTOPIV, A( 1, JPIVSTART ), LDA, IPIVSTART, J,
|
||||
$ IPIV, 1 )
|
||||
IPIVSTART = IPIVSTART - NTOPIV;
|
||||
NTOPIV = NTOPIV * 2;
|
||||
JPIVSTART = JPIVSTART - NTOPIV;
|
||||
END DO
|
||||
|
||||
* Permute U block to match L
|
||||
CALL DLASWP( KCOLS, A( 1,J+1 ), LDA, KSTART, J, IPIV, 1 )
|
||||
|
||||
* Factor the current column
|
||||
IF( A( J, J ).NE.ZERO .AND. .NOT.DISNAN( A( J, J ) ) ) THEN
|
||||
IF( ABS(A( J, J )) .GE. SFMIN ) THEN
|
||||
CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
|
||||
ELSE
|
||||
DO I = 1, M-J
|
||||
A( J+I, J ) = A( J+I, J ) / A( J, J )
|
||||
END DO
|
||||
END IF
|
||||
ELSE IF( A( J,J ) .EQ. ZERO .AND. INFO .EQ. 0 ) THEN
|
||||
INFO = J
|
||||
END IF
|
||||
|
||||
* Solve for U block.
|
||||
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', KAHEAD,
|
||||
$ KCOLS, ONE, A( KSTART, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA )
|
||||
* Schur complement.
|
||||
CALL DGEMM( 'No transpose', 'No transpose', M-J,
|
||||
$ KCOLS, KAHEAD, NEGONE, A( J+1, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA, ONE, A( J+1, J+1 ), LDA )
|
||||
END DO
|
||||
|
||||
* Handle pivot permutations on the way out of the recursion
|
||||
NPIVED = IAND( NSTEP, -NSTEP )
|
||||
J = NSTEP - NPIVED
|
||||
DO WHILE ( J .GT. 0 )
|
||||
NTOPIV = IAND( J, -J )
|
||||
CALL DLASWP( NTOPIV, A( 1, J-NTOPIV+1 ), LDA, J+1, NSTEP,
|
||||
$ IPIV, 1 )
|
||||
J = J - NTOPIV
|
||||
END DO
|
||||
|
||||
* If short and wide, handle the rest of the columns.
|
||||
IF ( M .LT. N ) THEN
|
||||
CALL DLASWP( N-M, A( 1, M+KCOLS+1 ), LDA, 1, M, IPIV, 1 )
|
||||
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', M,
|
||||
$ N-M, ONE, A, LDA, A( 1,M+KCOLS+1 ), LDA )
|
||||
END IF
|
||||
|
||||
RETURN
|
||||
*
|
||||
* End of DGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,277 +0,0 @@
|
||||
C> \brief \b SGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE SGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* REAL A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> SGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This code implements an iterative version of Sivan Toledo's recursive
|
||||
C> LU algorithm[1]. For square matrices, this iterative versions should
|
||||
C> be within a factor of two of the optimum number of memory transfers.
|
||||
C>
|
||||
C> The pattern is as follows, with the large blocks of U being updated
|
||||
C> in one call to STRSM, and the dotted lines denoting sections that
|
||||
C> have had all pending permutations applied:
|
||||
C>
|
||||
C> 1 2 3 4 5 6 7 8
|
||||
C> +-+-+---+-------+------
|
||||
C> | |1| | |
|
||||
C> |.+-+ 2 | |
|
||||
C> | | | | |
|
||||
C> |.|.+-+-+ 4 |
|
||||
C> | | | |1| |
|
||||
C> | | |.+-+ |
|
||||
C> | | | | | |
|
||||
C> |.|.|.|.+-+-+---+ 8
|
||||
C> | | | | | |1| |
|
||||
C> | | | | |.+-+ 2 |
|
||||
C> | | | | | | | |
|
||||
C> | | | | |.|.+-+-+
|
||||
C> | | | | | | | |1|
|
||||
C> | | | | | | |.+-+
|
||||
C> | | | | | | | | |
|
||||
C> |.|.|.|.|.|.|.|.+-----
|
||||
C> | | | | | | | | |
|
||||
C>
|
||||
C> The 1-2-1-4-1-2-1-8-... pattern is the position of the last 1 bit in
|
||||
C> the binary expansion of the current column. Each Schur update is
|
||||
C> applied as soon as the necessary portion of U is available.
|
||||
C>
|
||||
C> [1] Toledo, S. 1997. Locality of Reference in LU Decomposition with
|
||||
C> Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997),
|
||||
C> 1065-1081. http://dx.doi.org/10.1137/S0895479896297744
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is REAL array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE SGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.X) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
REAL A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
REAL ONE, ZERO, NEGONE
|
||||
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
|
||||
PARAMETER ( NEGONE = -1.0E+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
REAL SFMIN, TMP
|
||||
INTEGER I, J, JP, NSTEP, NTOPIV, NPIVED, KAHEAD
|
||||
INTEGER KSTART, IPIVSTART, JPIVSTART, KCOLS
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
REAL SLAMCH
|
||||
INTEGER ISAMAX
|
||||
LOGICAL SISNAN
|
||||
EXTERNAL SLAMCH, ISAMAX, SISNAN
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL STRSM, SSCAL, XERBLA, SLASWP
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN, IAND
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'SGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Compute machine safe minimum
|
||||
*
|
||||
SFMIN = SLAMCH( 'S' )
|
||||
*
|
||||
NSTEP = MIN( M, N )
|
||||
DO J = 1, NSTEP
|
||||
KAHEAD = IAND( J, -J )
|
||||
KSTART = J + 1 - KAHEAD
|
||||
KCOLS = MIN( KAHEAD, M-J )
|
||||
*
|
||||
* Find pivot.
|
||||
*
|
||||
JP = J - 1 + ISAMAX( M-J+1, A( J, J ), 1 )
|
||||
IPIV( J ) = JP
|
||||
|
||||
! Permute just this column.
|
||||
IF (JP .NE. J) THEN
|
||||
TMP = A( J, J )
|
||||
A( J, J ) = A( JP, J )
|
||||
A( JP, J ) = TMP
|
||||
END IF
|
||||
|
||||
! Apply pending permutations to L
|
||||
NTOPIV = 1
|
||||
IPIVSTART = J
|
||||
JPIVSTART = J - NTOPIV
|
||||
DO WHILE ( NTOPIV .LT. KAHEAD )
|
||||
CALL SLASWP( NTOPIV, A( 1, JPIVSTART ), LDA, IPIVSTART, J,
|
||||
$ IPIV, 1 )
|
||||
IPIVSTART = IPIVSTART - NTOPIV;
|
||||
NTOPIV = NTOPIV * 2;
|
||||
JPIVSTART = JPIVSTART - NTOPIV;
|
||||
END DO
|
||||
|
||||
! Permute U block to match L
|
||||
CALL SLASWP( KCOLS, A( 1,J+1 ), LDA, KSTART, J, IPIV, 1 )
|
||||
|
||||
! Factor the current column
|
||||
IF( A( J, J ).NE.ZERO .AND. .NOT.SISNAN( A( J, J ) ) ) THEN
|
||||
IF( ABS(A( J, J )) .GE. SFMIN ) THEN
|
||||
CALL SSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
|
||||
ELSE
|
||||
DO I = 1, M-J
|
||||
A( J+I, J ) = A( J+I, J ) / A( J, J )
|
||||
END DO
|
||||
END IF
|
||||
ELSE IF( A( J,J ) .EQ. ZERO .AND. INFO .EQ. 0 ) THEN
|
||||
INFO = J
|
||||
END IF
|
||||
|
||||
! Solve for U block.
|
||||
CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit', KAHEAD,
|
||||
$ KCOLS, ONE, A( KSTART, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA )
|
||||
! Schur complement.
|
||||
CALL SGEMM( 'No transpose', 'No transpose', M-J,
|
||||
$ KCOLS, KAHEAD, NEGONE, A( J+1, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA, ONE, A( J+1, J+1 ), LDA )
|
||||
END DO
|
||||
|
||||
! Handle pivot permutations on the way out of the recursion
|
||||
NPIVED = IAND( NSTEP, -NSTEP )
|
||||
J = NSTEP - NPIVED
|
||||
DO WHILE ( J .GT. 0 )
|
||||
NTOPIV = IAND( J, -J )
|
||||
CALL SLASWP( NTOPIV, A( 1, J-NTOPIV+1 ), LDA, J+1, NSTEP,
|
||||
$ IPIV, 1 )
|
||||
J = J - NTOPIV
|
||||
END DO
|
||||
|
||||
! If short and wide, handle the rest of the columns.
|
||||
IF ( M .LT. N ) THEN
|
||||
CALL SLASWP( N-M, A( 1, M+KCOLS+1 ), LDA, 1, M, IPIV, 1 )
|
||||
CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit', M,
|
||||
$ N-M, ONE, A, LDA, A( 1,M+KCOLS+1 ), LDA )
|
||||
END IF
|
||||
|
||||
RETURN
|
||||
*
|
||||
* End of SGETRF
|
||||
*
|
||||
END
|
||||
@@ -1,281 +0,0 @@
|
||||
C> \brief \b ZGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* INTEGER IPIV( * )
|
||||
* COMPLEX*16 A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* Purpose
|
||||
* =======
|
||||
*
|
||||
C>\details \b Purpose:
|
||||
C>\verbatim
|
||||
C>
|
||||
C> ZGETRF computes an LU factorization of a general M-by-N matrix A
|
||||
C> using partial pivoting with row interchanges.
|
||||
C>
|
||||
C> The factorization has the form
|
||||
C> A = P * L * U
|
||||
C> where P is a permutation matrix, L is lower triangular with unit
|
||||
C> diagonal elements (lower trapezoidal if m > n), and U is upper
|
||||
C> triangular (upper trapezoidal if m < n).
|
||||
C>
|
||||
C> This code implements an iterative version of Sivan Toledo's recursive
|
||||
C> LU algorithm[1]. For square matrices, this iterative versions should
|
||||
C> be within a factor of two of the optimum number of memory transfers.
|
||||
C>
|
||||
C> The pattern is as follows, with the large blocks of U being updated
|
||||
C> in one call to DTRSM, and the dotted lines denoting sections that
|
||||
C> have had all pending permutations applied:
|
||||
C>
|
||||
C> 1 2 3 4 5 6 7 8
|
||||
C> +-+-+---+-------+------
|
||||
C> | |1| | |
|
||||
C> |.+-+ 2 | |
|
||||
C> | | | | |
|
||||
C> |.|.+-+-+ 4 |
|
||||
C> | | | |1| |
|
||||
C> | | |.+-+ |
|
||||
C> | | | | | |
|
||||
C> |.|.|.|.+-+-+---+ 8
|
||||
C> | | | | | |1| |
|
||||
C> | | | | |.+-+ 2 |
|
||||
C> | | | | | | | |
|
||||
C> | | | | |.|.+-+-+
|
||||
C> | | | | | | | |1|
|
||||
C> | | | | | | |.+-+
|
||||
C> | | | | | | | | |
|
||||
C> |.|.|.|.|.|.|.|.+-----
|
||||
C> | | | | | | | | |
|
||||
C>
|
||||
C> The 1-2-1-4-1-2-1-8-... pattern is the position of the last 1 bit in
|
||||
C> the binary expansion of the current column. Each Schur update is
|
||||
C> applied as soon as the necessary portion of U is available.
|
||||
C>
|
||||
C> [1] Toledo, S. 1997. Locality of Reference in LU Decomposition with
|
||||
C> Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997),
|
||||
C> 1065-1081. http://dx.doi.org/10.1137/S0895479896297744
|
||||
C>
|
||||
C>\endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
C> \param[in] M
|
||||
C> \verbatim
|
||||
C> M is INTEGER
|
||||
C> The number of rows of the matrix A. M >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] N
|
||||
C> \verbatim
|
||||
C> N is INTEGER
|
||||
C> The number of columns of the matrix A. N >= 0.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in,out] A
|
||||
C> \verbatim
|
||||
C> A is COMPLEX*16 array, dimension (LDA,N)
|
||||
C> On entry, the M-by-N matrix to be factored.
|
||||
C> On exit, the factors L and U from the factorization
|
||||
C> A = P*L*U; the unit diagonal elements of L are not stored.
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[in] LDA
|
||||
C> \verbatim
|
||||
C> LDA is INTEGER
|
||||
C> The leading dimension of the array A. LDA >= max(1,M).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] IPIV
|
||||
C> \verbatim
|
||||
C> IPIV is INTEGER array, dimension (min(M,N))
|
||||
C> The pivot indices; for 1 <= i <= min(M,N), row i of the
|
||||
C> matrix was interchanged with row IPIV(i).
|
||||
C> \endverbatim
|
||||
C>
|
||||
C> \param[out] INFO
|
||||
C> \verbatim
|
||||
C> INFO is INTEGER
|
||||
C> = 0: successful exit
|
||||
C> < 0: if INFO = -i, the i-th argument had an illegal value
|
||||
C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
|
||||
C> has been completed, but the factor U is exactly
|
||||
C> singular, and division by zero will occur if it is used
|
||||
C> to solve a system of equations.
|
||||
C> \endverbatim
|
||||
C>
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
C> \author Univ. of Tennessee
|
||||
C> \author Univ. of California Berkeley
|
||||
C> \author Univ. of Colorado Denver
|
||||
C> \author NAG Ltd.
|
||||
*
|
||||
C> \date November 2011
|
||||
*
|
||||
C> \ingroup variantsGEcomputational
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )
|
||||
*
|
||||
* -- LAPACK computational routine (version 3.X) --
|
||||
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2011
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INFO, LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
INTEGER IPIV( * )
|
||||
COMPLEX*16 A( LDA, * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
COMPLEX*16 ONE, NEGONE
|
||||
DOUBLE PRECISION ZERO
|
||||
PARAMETER ( ONE = (1.0D+0, 0.0D+0) )
|
||||
PARAMETER ( NEGONE = (-1.0D+0, 0.0D+0) )
|
||||
PARAMETER ( ZERO = 0.0D+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
DOUBLE PRECISION SFMIN, PIVMAG
|
||||
COMPLEX*16 TMP
|
||||
INTEGER I, J, JP, NSTEP, NTOPIV, NPIVED, KAHEAD
|
||||
INTEGER KSTART, IPIVSTART, JPIVSTART, KCOLS
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
DOUBLE PRECISION DLAMCH
|
||||
INTEGER IZAMAX
|
||||
LOGICAL DISNAN
|
||||
EXTERNAL DLAMCH, IZAMAX, DISNAN
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL ZTRSM, ZSCAL, XERBLA, ZLASWP
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC MAX, MIN, IAND, ABS
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
* Test the input parameters.
|
||||
*
|
||||
INFO = 0
|
||||
IF( M.LT.0 ) THEN
|
||||
INFO = -1
|
||||
ELSE IF( N.LT.0 ) THEN
|
||||
INFO = -2
|
||||
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||||
INFO = -4
|
||||
END IF
|
||||
IF( INFO.NE.0 ) THEN
|
||||
CALL XERBLA( 'ZGETRF', -INFO )
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( M.EQ.0 .OR. N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Compute machine safe minimum
|
||||
*
|
||||
SFMIN = DLAMCH( 'S' )
|
||||
*
|
||||
NSTEP = MIN( M, N )
|
||||
DO J = 1, NSTEP
|
||||
KAHEAD = IAND( J, -J )
|
||||
KSTART = J + 1 - KAHEAD
|
||||
KCOLS = MIN( KAHEAD, M-J )
|
||||
*
|
||||
* Find pivot.
|
||||
*
|
||||
JP = J - 1 + IZAMAX( M-J+1, A( J, J ), 1 )
|
||||
IPIV( J ) = JP
|
||||
|
||||
! Permute just this column.
|
||||
IF (JP .NE. J) THEN
|
||||
TMP = A( J, J )
|
||||
A( J, J ) = A( JP, J )
|
||||
A( JP, J ) = TMP
|
||||
END IF
|
||||
|
||||
! Apply pending permutations to L
|
||||
NTOPIV = 1
|
||||
IPIVSTART = J
|
||||
JPIVSTART = J - NTOPIV
|
||||
DO WHILE ( NTOPIV .LT. KAHEAD )
|
||||
CALL ZLASWP( NTOPIV, A( 1, JPIVSTART ), LDA, IPIVSTART, J,
|
||||
$ IPIV, 1 )
|
||||
IPIVSTART = IPIVSTART - NTOPIV;
|
||||
NTOPIV = NTOPIV * 2;
|
||||
JPIVSTART = JPIVSTART - NTOPIV;
|
||||
END DO
|
||||
|
||||
! Permute U block to match L
|
||||
CALL ZLASWP( KCOLS, A( 1,J+1 ), LDA, KSTART, J, IPIV, 1 )
|
||||
|
||||
! Factor the current column
|
||||
PIVMAG = ABS( A( J, J ) )
|
||||
IF( PIVMAG.NE.ZERO .AND. .NOT.DISNAN( PIVMAG ) ) THEN
|
||||
IF( PIVMAG .GE. SFMIN ) THEN
|
||||
CALL ZSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
|
||||
ELSE
|
||||
DO I = 1, M-J
|
||||
A( J+I, J ) = A( J+I, J ) / A( J, J )
|
||||
END DO
|
||||
END IF
|
||||
ELSE IF( PIVMAG .EQ. ZERO .AND. INFO .EQ. 0 ) THEN
|
||||
INFO = J
|
||||
END IF
|
||||
|
||||
! Solve for U block.
|
||||
CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', KAHEAD,
|
||||
$ KCOLS, ONE, A( KSTART, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA )
|
||||
! Schur complement.
|
||||
CALL ZGEMM( 'No transpose', 'No transpose', M-J,
|
||||
$ KCOLS, KAHEAD, NEGONE, A( J+1, KSTART ), LDA,
|
||||
$ A( KSTART, J+1 ), LDA, ONE, A( J+1, J+1 ), LDA )
|
||||
END DO
|
||||
|
||||
! Handle pivot permutations on the way out of the recursion
|
||||
NPIVED = IAND( NSTEP, -NSTEP )
|
||||
J = NSTEP - NPIVED
|
||||
DO WHILE ( J .GT. 0 )
|
||||
NTOPIV = IAND( J, -J )
|
||||
CALL ZLASWP( NTOPIV, A( 1, J-NTOPIV+1 ), LDA, J+1, NSTEP,
|
||||
$ IPIV, 1 )
|
||||
J = J - NTOPIV
|
||||
END DO
|
||||
|
||||
! If short and wide, handle the rest of the columns.
|
||||
IF ( M .LT. N ) THEN
|
||||
CALL ZLASWP( N-M, A( 1, M+KCOLS+1 ), LDA, 1, M, IPIV, 1 )
|
||||
CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', M,
|
||||
$ N-M, ONE, A, LDA, A( 1,M+KCOLS+1 ), LDA )
|
||||
END IF
|
||||
|
||||
RETURN
|
||||
*
|
||||
* End of ZGETRF
|
||||
*
|
||||
END
|
||||
Reference in New Issue
Block a user